The wave function of a standing wave is y(x, t) = 4.44 mm sin[(32...

Question

The wave function of a standing wave is y(x, t) = 4.44 mm sin[(32.5 rad/m)x] sin[(754 rad/s)t]. For the two traveling waves that make up this standing wave, find the (c) frequency.

Accepted Answer

everyone in this problem? We have a wave traveling along a string. Ok? It's going to be totally reflected. So we have incident and reflective waves that produce a standing wave pattern and it's described by Y. X. Of T. Is equal to five centimeters sine of pi over four radiance per centimeter X. And sine of 30 pi radiance per second times T. Okay. And we're asked to find the frequency of the incident and reflected traveling waves. Okay, now first thing I want to recall is that when we're talking about frequency of reflected waves, the frequency of the incident and reflected wave will be the same. Okay, they're gonna have the same frequency when it gets reflected and maintains the same frequency. And so we only need to find one value. Okay, Okay, so we have our equation and let's recall the general form of the equation for a standing wave. In case we have Y. Of X. Of T. Is equal to to a sign. K. X. Sign. Oh my God. Okay. All right, so we're looking for frequency and we need to think about which of these is gonna be related to frequency. Well, let's recall that we know omega is equal to two pi F. Okay, so omega is going to equal two pi F. That's a relationship directly to frequency. And so let's figure out from our equation that were given what is omega. Well, let's look, omega is in the sign with the T case omega in our case is going to be this pi radiance for a second. Okay. And so we get 30 pi Oh my God. Okay. And on the right hand side we have two pi f. And if we divide we're going to be left with frequency is equal to 15 and we get inverse seconds. Okay? Which is equal to hurts rape. So the frequency is 15 hertz and that's the same frequency for the incident and the reflected traveling wave. That's it for this one. See you in the next video.

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